Some remarks on 'Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces'

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2014

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Springer international Publishing Ag

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

The main aim of this paper is to advise researchers in the field of Fixed Point Theory against an extended mistake that can be found in some proofs. We illustrate our claim proving that theorems in the very recent paper (Wang in Fixed Point Theory Appl. 2014: 137, 2014) are incorrect, and we provide different corrected versions of them.

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KARAPINAR, ERDAL/0000-0002-6798-3254; Roldán López de Hierro, Antonio Francisco/0000-0002-6956-4328

Keywords

fixed point, contractivity condition, isotone mapping, mixed monotone mapping

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3

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https://doi.org/10.1186/1687-1812-2014-245
 https://hdl.handle.net/20.500.14411/742

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